In addition to the video series xanthir recommended (which I also recommend, 3Blue1Brown is really good in general), I also recommend paul's math notes , a site that contains a lot of fairly in-depth explanations and examples for calculus(I believe there's there algebra too). iirc it also has proble...

Lately, I've been using Haskell quite a lot for solving Project Euler problems. Usually I'm done in a couple of lines (and hours of thinking, fiddling with expressions and debugging –debugging edge cases, mind you, there's no debugging of null pointers or anything) and the runner is done in a coupl...

Linear algebra is less about "lines and their equals" and more about vector spaces, and linear functions between them. Linear functions are functions that preserve vector addition and multiplication by a scalar. In linear algebra you'll learn what a vector space is, and you'll learn about ...

Looks cool from the video, and it has a demo so I can check it out when I get home! Excellent, let me know how it goes! Nice interface, although I could've gone with a smaller font size. I like that you added keybinding for the different modules, however I would like the ability to rebind keys(for ...

I'm going to be incredibly rude and necro this 7-year-old thread to post some news: I've made a new game! It's called Silicon Zeroes, it's a spiritual sequel to Manufactoria, and it's out right now on Steam and itch.io. Just a heads-up :) Looks cool from the video, and it has a demo so I can check ...

That solution reminds me of another riddle, where each of n participants is given a hat with a random color out one of n different colors(and what color one person gets is independent of what the rest get) and they need to form a strategy such that at least one of them must guess their own color cor...

Indeed it appears that none of Internet Explorer, Edge, and IE Mobile support the 'tab-size' CSS property, at least according to MDN's documentation. I guess Microsoft really want you to use a very specific tab-size, or else...

I can do it for you if it just come to the colors inside the circles (It will take me 30 minutes) but how could I replace the links (in yellow) between circles? After rethinking I believe that it will hard to guess the rules. So if no one find the rules (which is part of the puzzle) then I will pos...

Does DOS/Windows allow single quotes at all? I seem to remember it only liking double quotes, and wine cmd says "File not found" when I try to use single quotes with dir and type. Testing on a windows 10 machine: cmd.exe doesn't accept 'single quotes', only "double quotes". powe...

Funnily enough, Powershell handles tab-completion with files that have spaces in them just fine, it even automatically wraps the path in double quotes for you. Powetshell is far from perfect, but at least you can easily type /pro[tab, perhaps more than once] to get "C:\Program Files (x86)\&quot...

Something like that exists here in Norway [...]A giro: I buy something from you, you write a giro and give it to me. I hand in the giro to my bank, and the money moves from my bank to yours. What if you don't hand the giro to the bank? Jose I'd assume it'd result in either a lawsuit, or in the loss...

Keeping a list of my observations so far. ⋅ All shown outputs are prime or X ⋅ All shown outputs, where they are not X, are coprime to the inputs. ⋅ All integers of the form 6n+1 shown, except for 1, result in X ⋅ All other shown integers that result in X ...

Even better. As you guessed, Javascript will automatically add a semicolon at the end of a line if it makes syntactic sense. But then the brace becomes the start of a block statement, not the start of an object literal. Inside that block is the (useless) label "foo", on the (pointless) st...

I don't know much javascript but I am guessing line breaks act as statement separators(like semicolon), so the first one acts like return; essentially returning nothing, while the second one has an opening brace so it returns everything until the closing brace. I am guessing that's because javascrip...

Yes! That is a valid argument, and a perfect example of proof by induction. You have the base step, the induction step, and you correctly justify your conclusion using known properties of even and odd numbers. But my argument still contains an assumption that I'd need to build out (I think), which ...

The first sentence you wrote just reiterates the definition of an even number. You gave no justification for why every integer that isn't even to be odd, since odd means 1 greater than an even number. The proof by induction provides such justification. I have to start somewhere. By necessity, becau...

The first sentence you wrote just reiterates the definition of an even number. You gave no justification for why every integer that isn't even to be odd, since odd means 1 greater than an even number. The proof by induction provides such justification.

What background knowledge? Do you have some other proof that every integer is either even or odd? Remember that "n is even" means "there exists m such that n=2m" and "n is odd" means "there exists m such that n=2m+1" Did you ever prove the statement "ever...

:arrow: It's pedagogically useful. It is nice to practice proof by induction if you do not understand induction by using it to prove things which you can already understand and prove by another means. I would agree with that, but the problem with the even-odd example is that it doesn't (at least in ...

Proof by induction is usually useful when you want to prove some statement about all integers greater than or equal to some starting value. The original problem in this thread has the statement "1+2+3+...+(n-1)+n=n(n+1)/2" The even-odd problem has the statement "n is even or n is odd&...

I'll just leave this here. It's the post I posted a page ago and was completely ignore by mathdofus. I ask that you read this post, if you hit a point you don't understand, write down what you don't understand on a piece of paper and continue reading, writing the points you don't understand. Then re...

The tutorials and books Xanthir linked are aimed at people who have no programming backgroud, so they should teach you, along with the specifics of the python language, how programming works. I didn't check them all but they probably include example problems and solutions(using python). Once you hav...

But you don't seem to know how to prove them, which is what we're doing here. We keep circling around this same problem. The induction step is just a conditional proof. If I demonstrate that a base case is true, and then demonstrate that if the k case is true then the (k + 1) case is true, then I'v...

It's a proof by induction of the statement "every natural number n is either even or odd" Another, simpler(and pretty trivial) proof by induction would be "every positive natural number n is divisible by 1" To prove that by induction, we follow the basic steps of induction: Base ...

While I am not too well versed in python, I think it is better for you to think about these functions as procedures, or subroutines, basically they are there to divide up your code and eliminate a lot of rewriting code. Some languages allow passing functions as arguments to other functions, which ma...

Well, a bigger ∘ fits with union and intersection notation, and I believe ∘ is closer to sets than to numbers. I also recall seeing + and × used instead of the sigma and pi somewhere - oh right it was a Youtube video talking about notation...